-This paper presents a low power and low-voltage analog switched-current (SI) filters implementation of wavelet transform (WT) for real-time requirements in signal processing. First, an adaptive genetic algorithm (AGA) is used to calculate the transfer function of the filters, whose impulse response is the required wavelet base. This approach improves the approximation performance than the previous traditional approaches and allows for the circuit implementation of any other wavelet base. Next, the approximation wavelet function is implemented using SI filters based on the cascade structure with SI differentiators as main building blocks. The Gaussian wavelet is selected as an example to illustrate the design procedure. Simulations demonstrate that the proposed method implements WT is an excellent way.Index Terms -Wavelet transform, analog filters, analog implementation, switched-current differentiators, adaptive genetic algorithms.
I . IntroductionThe WT has been a very promising mathematical tool for signal processing, due to its good estimation of time and frequency localizations [1]. The WT is traditionally implemented using digital circuits. However, for low-power, low-voltage and real-time applications, it is not suitable to implement the WT due to the high power consumption and large area associated with the required A/D (analog-digital) converter. Consequently, the analog WT implementations have been an attractive field in signal processing.Recently, some significant advances for implementing WT with analog filters have been introduced in the literatures [2][3][4][5][6][7][8][9][10][11]. Among, the implementations using analogue sampled-data circuits have attracted much attention [2,[8][9][10][11]. A key feature of using these circuits for implementing WT is that dilation constant across different scales may be easily and precisely controlled by the clock frequencies. Typically, the switchedcapacitors (SC) circuit has been used to implement analog WT [2]. However, the SC circuits are not fully compatible with current trends in digital CMOS process and their performance suffers as supply voltages are scaled down. To resolve these problems, the SI circuit [8-11] is applied to implement WT. The SI WT circuits consist of analog filters whose impulse response is the approximated wavelet and its dilations. So the performance of the WT realization depends largely on the approximation accuracy of the wavelet function. In the proposed approximation methods, Padé approximation [3,8] is employed to approximate the Laplace transform of the desired wavelet filter transfer function. However, (1) the stable transfer function of a wavelet filter does not automatically result from the Padé approximation, (2) the choice of the degrees for the numerator and denominator polynomials in the approximation transfer function is difficult, (3) the wavelet approximation is only obtained directly in the Laplace domain, but not in the time domain. L 2 approximation [4,5,6,9], in order to find a suitable wavelet base approxi...